When a cannon with a longer barrel is fired, the force of expanding gases acts on the cannonball for a longer distance. What effect does this have on the velocity of the emerging cannonball? (Do you see why long-range cannons have such long barrels?)
Please help; need a original answer no Google search. Thank you in advance...
Certainly! When a cannon is fired, the force of expanding gases generated by the gunpowder propellant propels the cannonball out of the barrel. The force acts on the cannonball for a certain amount of time, known as the duration of the force application.
In a cannon with a longer barrel, the expanding gases have more time to act on the cannonball since it must travel a greater distance before exiting the barrel. This means that the duration of the force application is longer in a longer barrel.
According to Newton's second law of motion, force is equal to the rate of change of momentum. Assuming the mass of the cannonball remains constant, a longer duration of force application leads to a greater change in momentum, and hence a greater final velocity for the emerging cannonball.
Therefore, the longer barrel allows the cannonball to be propelled with a higher velocity. This increased velocity contributes to the long-range capability of cannons as the higher speed enables the projectile to cover larger distances and reach targets further away.
Hence, the design of long-range cannons with longer barrels is intended to take advantage of the increased duration of force application, resulting in higher velocities and improved range.